Help needed with customising 'thematic_postheader()'

I'm gradually getting a hang of this. I'm right in the middle of developing a custom theme for my site [soon enough I'll be able to showcase this] locally. With each turn, one seems to realize that they just need some extra input/ explanation.

As such, I need some help with customising 'thematic_postheader()' as follows:
- Supress [omit] the 'By Author'
- Show the date only [omit the 'published' text]
- Show the date just besides, but before, the title